Mesh Quality Improvement Research Articles

Adaptively Isotropic Remeshing Based on Curvature Smoothed Field.

With the development of 3D digital geometry technology, 3D triangular meshes are becoming more useful and valuable in industrial manufacturing and digital entertainment. A high quality triangular mesh can be used to represent a real world object with geometric and physical characteristics. While anisotropic meshes have advantages of representing shapes with sharp features (such as trimmed surfaces) more efficiently and accurately, isotropic meshes allow more numerically stable computations. When there is no anisotropic mesh requirement, isotropic triangles are always a good choice. In this paper, we propose a remeshing method to convert an input mesh into an adaptively isotropic one based on a curvature smoothed field (CSF). With the help of the CSF, adaptively isotropic remeshing can retain the curvature sensitivity, which enables more geometric features to be kept, and avoid the occurrence of obtuse triangles in the remeshed model as much as possible. The remeshed triangles with locally isotropic property benefit various geometric processes such as neighbor-based feature extraction and analysis. The experimental results show that our method achieves better balance between geometric feature preservation and mesh quality improvement compared to peers. We provide the implementation codes of our resampling method at github.com/vvvwo/Adaptively-Isotropic-Remeshing.

A Delaunay refinement algorithm for the particle finite element method applied to free surface flows

AbstractThis article proposes two contributions to the calculation of free‐surface flows using the particle finite element method (PFEM). The PFEM is based upon a Lagrangian approach: a set of particles defines the fluid and each particle is associated with a velocity vector. Then, unlike a pure Lagrangian method, all the particles are connected by a triangular mesh. The difficulty lies in locating the free surface from this mesh. It is a matter of deciding which of the elements in the mesh are part of the fluid domain, and to define a boundary—the free surface. Then, the incompressible Navier–Stokes equations are solved on the fluid domain and the particle position is updated using the velocity vector from the finite element solver. Our first contribution is to propose an approach to adapt the mesh with theoretical guarantees of quality: the mesh generation community has acquired a lot of experience and understanding about mesh adaptation approaches with guarantees of quality on the final mesh. The approach we use here is based on a Delaunay refinement strategy, allowing to insert and remove nodes while gradually improving mesh quality. We show that what is proposed allows to create stable and smooth free surface geometries. One characteristic of the PFEM is that only one fluid domain is modeled, even if its shape and topology change. It is nevertheless necessary to apply conditions on the domain boundaries. When a boundary is a free surface, the flow on the other side is not modeled, it is represented by an external pressure. On the external free surface boundary, atmospheric pressure can be imposed. Nevertheless, there may be internal free surfaces: the fluid can fully encapsulate cavities to form bubbles. The pressure required to maintain the volume of those bubbles is a priori unknown. For example, the atmospheric pressure would not be sufficient to prevent the bubbles from deflating and eventually disappearing. Our second contribution is to propose a multi‐point constraint approach to enforce global incompressibility of those empty bubbles. We show that this approach allows to accurately model bubbly flows that involve two fluids with large density differences, for instance water and air, while only modeling the heavier fluid.

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

Evolutionary multi-objective high-order tetrahedral mesh optimization

High-order mesh optimization has many goals, such as improving smoothness, reducing approximation error, and improving mesh quality. The previous methods do not optimize these objectives together, resulting in suboptimal results. To this end, we propose a multi-objective optimization method for high-order meshes. Central to our algorithm is using the multi-objective genetic algorithm (MOGA) to adapt to the multiple optimization objectives. Specifically, we optimize each control point one by one, where the MOGA is applied. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves a favorable trade-off between multiple objectives.

Modal and fatigue characteristics analysis of key components of tower crane

In order to ensure good stability and safety of the tower crane under long-term heavy load conditions, modal analysis and fatigue analysis were conducted on its key components, including standard section and frame section. The connection points of each truss structure were regarded as indivisible common nodes, and the model was simplified and parameterized, resulting in improved mesh quality and computational efficiency. Based on Pro/E, standard section and frame section models were established and imported into Workbench through intermediate data formats for simulation calculations in modal and static structural modules. By calculation, the natural frequency and modal shape of the standard section, as well as the lifespan, damage, and safety factor of the frame section, were obtained. It can be seen that the standard section has good structural stability and can maintain relative balance under excitation in different directions and degrees of freedom. If the safety factor of the web components is high and the service life is improved from a structural perspective, it can be considered to increase the thickness of the chord members.

An adaptive anisotropic bilateral filtering method for mesh data in scale space

Three-dimensional mesh data of parts, such as blades and engine bodies, have been widely used in industrial fields. Due to the different kinds of noise during mesh acquisition and the machining deficiency of parts, the mesh quality tends to be insufficient for subsequent operations. Therefore, mesh denoising is a necessary and critical procedure to improve mesh quality. Existing methods commonly apply geometry features smoothing, which may also create unexpected results, such as volume shrinkage and blurring of sharp edges. This paper proposed an adaptive anisotropic bilateral filtering method for mesh data in scale space. Firstly, the mesh is decomposed into a smooth base with low frequency and a height vector field with high frequency based on scale space theory. The denoising of the vertex spatial field is transformed into the denoising of the height vector field, aiming to only consider high-frequency information. Secondly, the bilateral filter scheme with the anisotropic Gaussian kernel is proposed to denoise the height vector field, removing noise mixed with features. The parameters in the bilateral filter scheme are chosen adaptively by maximizing the designed probability density function. The mean square angular error of the proposed method is less than 0.15 rad, which is superior to the general-purpose algorithms, for instance, Laplacian filtering, bilateral mesh filtering and bilateral normal filtering algorithm.

Numerical study of heat transfer characteristics of phase change materials reinforced with porous media based on hybrid mesh

To address the drawbacks of inadequate energy density as well as utilization effectiveness in solar energy utilization, phase change energy storage offers a possible option. However, the low thermal conductivity of traditional phase change materials (PCMs) restricts the extent to which solar energy utilization can be enhanced. In this paper, the impact of the metal foam (MF) on the solid–liquid interface, the flow field, the enhancement heat transfer mechanism during the paraffin wax (PX) melting process and thermal storage characteristics was analyzed. Besides, a three-dimensional mathematical model of MF-PX using the hybrid mesh technique was established and software ANSYS-FLUENT was used for simulation. The results indicated that, the hybrid mesh exhibited a reduction of 52.75 % in mesh count compared to the unstructured mesh, resulting in 45 % reduction in computational time. Moreover, the hybrid mesh also showcased improved mesh quality that the unstructured mesh was mainly distributed in the range of 0.48–0.6, while within the range of 0.84–1.0 for the hybrid mesh. More important, the maximum relative error between experimental and simulation was 8.67 %, indicating that the model can make a reasonable prediction. With the proportions of MF increased from 0.11 % to 0.43 %, both the Rayleigh number (Ra) and its amplification decreased. At 800 s, the Ra decreased from 1.76E+07 to 1.20E+07, while the amplification of the Ra was reduced from 1.88E+07 to 1.30E+07. In addition, the natural convection proportions of CMF decreased from 96.31 % to 80.65 %. These observations indicated that natural convection was the primary heat transfer mechanism, and the conduction was enhanced by the increasing proportion of MF. Finally, in terms of heat storage characteristics, the heat storage capacity and heat storage rate of the composite PCM slightly decreased. The heat storage values decreased from 19.30 kJ to 18.66 kJ. Similarly, the heat storage rates decreased from 19.86 J/s to 18.81 J/s.

Hexahedral Mesh Quality Improvement with Geometric Constraints

Hexahedral Mesh Quality Improvement with Geometric Constraints

Planar Delaunay Mesh Smoothing Method Based on Angle and a Deep Q-Network

Mesh quality is critical to the accuracy and efficiency of finite element calculations, and mesh smoothing is an essential means of reducing the number of poor elements and improving mesh quality. The deep Q-network-based optimization algorithm for planar Delaunay mesh (unconstrained DQN) has attracted increasing attention due to its advantages in autonomous optimization. However, the unconstrained DQN model does not constrain the movement area of the central node during the training process, and element quality easily falls into a local optimum, resulting in a low generalization of the DQN model. In this paper, an updateable iterative inner polygon is proposed as a constraint to limit the central node’s movement and control the element’s angle. Next, the performance of different neural networks when training the same dataset is analyzed, and the appropriate neural network is selected. After that, the effectiveness and generalization of the method were analyzed. Finally, the results were compared with those obtained by existing methods. The results show that the proposed algorithm can improve the minimum angle of global elements and the shape of poor elements, and the trained DQN model has a high generalization.

SRL-assisted AFM: Generating planar unstructured quadrilateral meshes with supervised and reinforcement learning-assisted advancing front method

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual processing and has long been considered the most challenging and time-consuming bottleneck of the entire modeling and analysis process. In this paper, we present a novel computational framework named “SRL-assisted AFM” for meshing planar geometries by combining the advancing front method with neural networks that select reference vertices and update the front boundary using “policy networks”. These deep neural networks are trained using a unique pipeline that combines supervised learning with reinforcement learning to iteratively improve mesh quality. First, we generate different initial boundaries by randomly sampling points in a square domain and connecting them sequentially. These boundaries are used for obtaining input meshes and extracting training datasets in the supervised learning module. We then iteratively improve the reinforcement learning model performance with reward functions designed for special requirements, such as improving the mesh quality and controlling the number and distribution of extraordinary points. Our proposed supervised learning neural networks achieve an accuracy higher than 98% on predicting commercial software. The final reinforcement learning neural networks automatically generate high-quality quadrilateral meshes for complex planar domains with sharp features and boundary layers.

Isogeometric analysis of acoustic scattering with perfectly matched layers (IGAPML)

The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced further using the isogeometric framework. This work presents a spline based PML formulation which avoids additional coordinate transformation as the formulation is based on the same space in which the numerical solution is sought. The procedure can be automated for any convex artificial boundary. This removes restrictions on the domain construction using PML and can therefore reduce computational cost and improve mesh quality. The usage of spline basis functions with higher continuity also improves the accuracy of the PML-approximation and the numerical solution.

A Parallel Variational Mesh Quality Improvement Method for Tetrahedral Meshes Based on the MMPDE Method

There are numerous large-scale applications requiring mesh adaptivity, e.g., cardiac electrophysiology, computational fluid dynamics, fracture propagation, and weather prediction. Parallel processing is needed for simulations involving large-scale adaptive meshes. In this paper, we propose a parallel variational mesh quality improvement algorithm for use with distributed memory machines. Our parallel method is based on the sequential method by Huang, Ren, and Russell and the recent implementation by Huang and Kamenski. Their approach is based on the use of the Moving Mesh PDE method to adapt the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ordinary differential equations (ODEs) to be solved which determine where to move the interior mesh nodes. The MMPDE method successfully removes/reduces the number of extreme dihedral angles, particularly those less than 2 0 o or greater than 15 0 o . An efficient solution is obtained by solving the ODEs on subregions of the mesh with overlapped communication and computation. Strong and weak scaling experiments on up to 128 cores for meshes with up to 160M elements demonstrate excellent results. • A parallel algorithm and implementation are proposed for variational mesh quality improvement on simplicial meshes. This is the first parallel variational mesh quality improvement method. • The method is based on the sequential moving mesh PDE (MMPDE) method of Huang, Ren, and Russell and the recent implementation by Huang and Kamenski which removes or significantly reduces the number of extreme dihedral angles in a tetrahedral mesh upon smoothing. • Their approach adapts the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ODEs to be solved for the velocities of the interior mesh nodes. • An efficient solution is obtained by solving the ODEs in parallel on subregions of the mesh with overlapped communication and computation. • Excellent scalability results are obtained on up to 128 cores for tetrahedral meshes with up to 160M elements and on an industrial example from the tire industry.

A target construction methodology for mesh quality improvement

A target construction methodology for mesh quality improvement

Simultaneous shape and mesh quality optimization using pre-shape calculus

Abstract Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.

An efficient method to improve the quality of tetrahedron mesh with MFRC

In this paper, we proposed a novel operation to reconstruction tetrahedrons within a certain region, which we call MFRC (Multi-face reconstruction). During the existing tetrahedral mesh improvement methods, the flip operation is one of the very important components. However, due to the limited area affected by the flip, the improvement of the mesh quality by the flip operation is also very limited. The proposed MFRC algorithm solves this problem. MFRC can reconstruct the local mesh in a larger range and can find the optimal tetrahedron division in the target area within acceptable time complexity. Therefore, based on the MFRC algorithm, we combined other operations including smoothing, edge removal, face removal, and vertex insertion/deletion to develop an effective mesh quality improvement method. Numerical experiments of dozens of meshes show that the algorithm can effectively improve the low-quality elements in the tetrahedral mesh, and can effectively reduce the running time, which has important significance for the quality improvement of large-scale mesh.

Error-bounded Edge-based Remeshing of High-order Tetrahedral Meshes

We present a robust method to generate high-quality high-order tetrahedral meshes with bounded approximation errors and low mesh complexity. The success of our method relies on two key components. The first one is three novel local operations that robustly modify the topology of the high-order tetrahedral mesh while avoiding invalid (flipped or degenerate) elements. In practice, our meshing algorithm follows the edge-based remeshing algorithm that iteratively conducts these local topological operations and a geometric optimization operation to improve mesh quality. The second is a new containment check procedure that robustly judges whether the approximation error between the input mesh and the high-order mesh exceeds the user-specified bound. If one operation causes the error-bounded constraint to be violated, we reject this operation to ensure a bounded approximation error. Besides, the number of tetrahedrons of the high-order mesh is reduced by progressively increasing the target edge length in the edge-based remeshing algorithm. A large number of experimental results have shown the capability and feasibility of our method. Compared to other state-of-the-art methods, our method achieves higher robustness and quality.

Designing Parallel Adaptive Laplacian Smoothing for Improving Tetrahedral Mesh Quality on the GPU

Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios.

Numerical prediction of slurry erosion and its influence on prevailing flow conditions using a dynamic mesh method

With the help of Computational Fluid Dynamics (CFD), the amount and location of slurry erosion can be predicted using renowned models. However, all common models do not change the hydraulic contour of the system and can therefore be interpreted as a CFD-post-processing step. Thus, the influence of slurry erosion on the fluid flow is currently not considered and the effects of changing flow conditions on the system performance or perhaps energy efficiency are not predictable. Building upon this state of the art, a numerical method based on the idea of a dynamic mesh procedure is developed. The method uses the predicted erosion to locally deform the mesh during simulation. The method contains the generation of an array-based mesh structure, the precise movement of affected boundary nodes including the tracking of inner nodes as well as a reconstructing procedure to improve mesh quality after deformation. The whole method is implemented in a commercial CFD-code. The functionality of the method is examined using the example of a standardized water pump. The comparison to corresponding experimental results revealed an accurate prediction of the erosion distribution in the pump’s front casing. Furthermore, the evaluation of the pump’s performance curves indicated an accurate prediction of the changing flow field caused by erosive wear.

Structure-aware completion of photogrammetric meshes in urban road environment

Photogrammetric mesh models obtained from aerial oblique images have been widely used for urban reconstruction. However, photogrammetric meshes suffer from severe texture problems, particularly in typical road areas, owing to occlusion. This paper proposes a structure-aware completion approach to improve mesh quality by seamlessly removing undesired vehicles. Specifically, a discontinuous texture atlas is first integrated into a continuous screen space by rendering trough a graphics pipeline. The rendering also records the necessary mapping for deintegration to the original texture atlas after editing. Vehicle regions are masked by a standard object detection approach, namely, Faster RCNN. Subsequently, the masked regions are completed, guided by the linear structures and regularities in the road region; this is implemented based on PatchMatch. Finally, the completed rendered image is deintegrated to the original texture atlas, and the triangles for the vehicles are also flattened so that improved meshes can be obtained. Experimental evaluation and analysis are conducted on three datasets, which were captured with different sensors and ground sample distances. The results demonstrate that the proposed method can produce quite realistic meshes after removing the vehicles. The structure-aware completion approach for road regions outperforms popular image completion methods, and an ablation study further confirms the effectiveness of the linear guidance. It should be noted that the proposed method can also handle tiled mesh models for large-scale scenes. Code and datasets are available at the project website11https://vrlab.org.cn/hanhu/projects/mesh.

Static mesh adaptation for reliable large eddy simulation of turbulent reacting flows

The design challenge of reliable lean combustors needed to decrease pollutant emissions has clearly progressed with the common use of experiments as well as large eddy simulation (LES) because of its ability to predict the interactions between turbulent flows, sprays, acoustics, and flames. However, the accuracy of such numerical predictions depends very often on the user's experience to choose the most appropriate flow modeling and, more importantly, the proper spatial discretization for a given computational domain. The present work focuses on the last issue and proposes a static mesh refinement strategy based on flow physical quantities. To do so, a combination of sensors based on the dissipation and production of kinetic energy coupled to the flame-position probability is proposed to detect the regions of interest where flow physics happens and grid adaptation is recommended for good LES predictions. Thanks to such measures, a local mesh resolution can be achieved in these zones improving the LES overall accuracy while, eventually, coarsening everywhere else in the domain to reduce the computational cost. The proposed mesh refinement strategy is detailed and validated on two reacting-flow problems: a fully premixed bluff-body stabilized flame, i.e., the VOLVO test case, and a partially premixed swirled flame, i.e., the PRECCINSTA burner, which is closer to industrial configurations. For both cases, comparisons of the results with experimental data underline the fact that the predictions of the flame stabilization, and hence the computed velocity and temperature fields, are strongly influenced by the mesh quality and significant improvement can be obtained by applying the proposed strategy.